Demonstration of electric micropropulsion multimodality

Electric propulsion has become popular nowadays owing to the trend of miniaturizing the size and mass of satellites. However, the main drawback of the most popular approach—Hall thrusters—is that their efficiency and thrust-to-power ratio (TPR) markedly deteriorate when its size and power level are reduced. Here, we demonstrate an alternative approach—a minute low-power (<50 W), lightweight (~100 g), two-stage propulsion system. The system is based on a micro-cathode vacuum arc thruster with magnetoplasmadynamic second stage (μCAT-MPD), which achieves the following parameters: a thrust of up to 1.7 mN at a TPR of 37 μN/W and an efficiency of ~50%. A μCAT-MPD system, in addition to “traditional” inverse, displays the anomalous direct (growing) “TPR versus specific impulse Isp” trend at high Isp values and allows multimodality at high efficiency.

where τ 1 , τ 1 are the pulse widths of the first-and second-stage instantaneous powers. The errors for P 1 , P 2 were estimated as standard deviations δ(P 1 ), δ(P 2 ) over up to 6 experimental trials. The total power P dissipated in the both stages within single experimental trial was estimated by summarizing P 1 and P 2 : The error for P was estimated using the standard deviations δ(P 1 ), δ(P 2 ) for the first and secondstage powers: The final value of the total power P was obtained as the average value of all experimental total powers P obtained at the same experimental conditions.
Thrust and thrust-to-power ratio The average thrust was measured by placing the thruster directly on the movable arm of the torsional thrust stand (see the Fig. S2). Thruster firing caused the deflection of the movable arm around its axis of rotation; this deflection was measured by the laser sensor. Using the set of fins placed on high-precision scale (identical to the fins placed on the end of the thrust stand arm), this deflection was recalculated to a force (i.e. thrust). More detailed information regarding thrust stand measurements are given in our previous work ( ). The final value of the average thrust T then was estimated as the average value of thrusts T obtained within up to 6 experimental trials at the same experimental parameters. The error of thrust T was estimated as a standard deviation δ(T).
The thrust-to-power ratio (TPR) was measured by dividing the thrust value T over the total power P : The error for TPR was estimated using relative errors of the standard deviations for thrust δ(T) and total power δ(P): where TPR , T and P are the average values of thrust-to-power ratio, thrust and power for the same experimental conditions.

Exhausting ion velocity
The exhausting ions velocity was determined by the time-of-flight method using experimental setup described in details in our previous study (35). Briefly, the thruster was fired with the plasma towards the two negatively-biased electrodes (first one is copper grid, the last one is stainless steel plate) placed at the distances s 12 = 17 cm and s 13 = 37 cm from the thruster exhaust. Once ions arrive at the electrode, they produce a pulsing current in the circuits of the each electrode. The ion velocity within single experiment v was estimated as: where s 12 is the distance between the thruster exhaust and the first electrode, s 23 is the distance between electrodes, s 13 is the distance between the thruster exhaust and the last electrode, t 12 , t 23 and t 13 are respective time delays between maxima of the first-stage discharge current and ionic currents from each electrode. The final value of the ion velocity v was estimated as the average value of velocities v obtained within up to 6 experimental trials at the same experimental parameters. The error of ion velocity v was estimated as a standard deviation δ(v).
Total ion current measurement Total ion current I i (t) was measured by placing the thruster inside a semispherical negativelybiased (-100 V) electrode (2 , 35). Then, the fractions of pulse-average total current i I and charge i Q of ions expelled by the thruster were estimated using the formulas: where τ i is the duration of the total ion current pulse, Q 1 and Q 2 are the charges of the first-and second-stage discharge currents. The error in determination of the mentioned ratios was estimated to the respective standard deviations.